Using mathutils.geometry.box_fit_2d
The angle returned by box_fit_3d is the angle by which the given points have to be rotated to best fit them into a rectangle aligned with the axes. 

The example script linked in your question – currently there is only one script with a call to box_fit_3d – does indeed use the angle to calculate the coordinates of the rotated points: 

angle = mathutils.geometry.box_fit_2d(cos_2d)

mat = mathutils.Matrix.Rotation(angle, 2)
cos_2d = [(mat * co) for co in cos_2d]
xs = [co.x for co in cos_2d]
ys = [co.y for co in cos_2d]


But if you instead want to fit the original points into a rotated rectangle then you would have to rotate the rectangle by the negative of that angle.
The image below shows the face from your question together with a plane rotated by −50.005 degrees instead.



If you're also interested in the optimal size of the rectangle I guess it's still best to calculate the rotated points and then determine the smallest and largest coordinates like it's been done in the example script. 

width = max(xs) - min(xs)
height = max(ys) - min(ys)